2D CA are most popularly emulated on a square grid {4,4}, and occasionally on the hexagonal grid {6,3}. There exist one more proper tiling {3,6}, the triangular tiling, which can also be used to simulate cellular automata. LifeViewer has had support for range-1 triangular CA for almost a year now, but this feature hasn't seen nearly enough use, so it's probably a good idea to spark discussion of these rules so the implementation doesn't go to waste.

Obligatory parity/replication rules:

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```
x = 1, y = 1, rule = B13579Y/S13579YL
o!
```

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```
x = 1, y = 1, rule = B13579Y/S02468XZL
o!
```

For the Triangular Edges neighbourhood, it can be noted that these mimic the behaviour of the hexagonal parity rules on even generations:

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```
x = 1, y = 1, rule = B13/S02LE
o!
```

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```
x = 1, y = 1, rule = B135/S135H
o!
```

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```
x = 1, y = 1, rule = B13/S13LE
o!
```

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```
x = 1, y = 1, rule = B135/S0246H
o!
```

FredkinModN.py allows for generalisation of parity rules like with other neighbourhoods (even if attempting to generate higher order moore ones does murdery things to the computer):

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```
x = 1, y = 1, rule = Fredkin mod3 triangularVonNeumann emulated
o!
```

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```
x = 1, y = 1, rule = Fredkin mod5 triangularVonNeumann emulated
o!
```

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```
x = 1, y = 1, rule = Fredkin mod7 triangularVonNeumann emulated
o!
```

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```
x = 1, y = 1, rule = Fredkin mod11 triangularVonNeumann emulated
o!
```

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```
x = 1, y = 1, rule = Fredkin mod13 triangularVonNeumann emulated
o!
```

Spaceships can exist in triangular rules like with most other rulespaces. For example, here are the spaceships from the trilife package on the golly rule repository:

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```
x = 4, y = 2, rule = B4/S456L
4o$4o!
```

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```
x = 7, y = 4, rule = B45/S23L
5bo$o3b3o$o3b3o$5bo!
```

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```
x = 8, y = 3, rule = B45/S34L
5bobo$3o2b3o$3o3b2o!
```

as well as the following ship provided in the triangular lifeviewer demo:

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```
x = 8, y = 6, rule = B456/S34L
bo3bo$bo4bo$b2o4bo$2bo5bo$2bo5bo$3b2ob2o!
```

The demo also shows a triangular generations rule with interesting dynamics including a common unloopable RRO:

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```
x = 8, y = 6, rule = G10/B34/S34L
bo3bo$bo4bo$b2o4bo$2bo5bo$2bo5bo$3b2ob2o!
[[ THEME Blues ]]
```

I haven't tried creating an isotropic non-totalistic notation for the triangular grid, and it'd probably be significantly bigger than the current square moore non totalistic notation, and maybe bigger than range 2 vN and also the range 1 3 state notation I'm currently busy with. I might do so in the future though.

Please discuss further!